Question: Rewrite as a simplified fraction. ${0.\overline{36} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 36.3636...\\ 1x &= 0.3636...\end{align*}}$ Subtracting the two equations, we have: ${99x = 36}$ ${x = \dfrac{36}{99}} $ ${x = \dfrac{4}{11}} $